Consider a strategic game G = (S1,...,Sn;u1,...,un). 1.Suppose p and q are strategies for player 1, and let [0,1]. Show that p + (1)q is also a strategy for player 1.

2.More generally, show that any convex combination of strategies is again a strategy.

3.A strategy p for player 1 is optimal with respect to strategies p2, ..., pn for the other players, if it maximizes the expected payo for player 1. Prove that a convex combination of optimal strategies is again optimal